قطر دایره $BC\Rightarrow \overset\frown{BAC}=180=\overset\frown{BA}+\overset\frown{AC}\Rightarrow 180=120+\overset\frown{AC}\Rightarrow \overset\frown{AC}=60{}^\circ $ محاطی $\widehat{B}=\frac{\overset\frown{AC}}{2}=30{}^\circ $  $\widehat{B}=30\Rightarrow OH=\frac{1}{2}OB$ $OH=\frac{x}{2}$  $OB=X\to {{3}^{2}}+\frac{{{X}^{2}}}{2}={{X}^{2}}\Rightarrow 9+\frac{{{X}^{2}}}{4}={{X}^{2}}\Rightarrow 9=\frac{3{{X}^{2}}}{4}\Rightarrow {{X}^{2}}=\frac{36}{3}\Rightarrow X=\frac{6}{\sqrt{3}}$  $OB=X$  $HB=3$